Tomáš Bárta (2013)
Open Mathematics
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We show global existence for a class of models of fluids that change their properties depending on the concentration of a chemical. We allow that the stress tensor in (t, x) depends on the velocity and concentration at other points and times. The example we have in mind foremost are materials with memory.
Gao, Hongjun, Ma, To Fu (1999)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Jong Yeoul Park, Sun Hye Park (2009)
Czechoslovak Mathematical Journal
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We prove the existence and uniform decay rates of global solutions for a hyperbolic system with a discontinuous and nonlinear multi-valued term and a nonlinear memory source term on the boundary.
F. Guillén-González (2004)
Czechoslovak Mathematical Journal
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We study the system of PDEs describing unsteady flows of incompressible fluids with variable density and non-constant viscosity. Indeed, one considers a stress tensor being a nonlinear function of the symmetric velocity gradient, verifying the properties of -coercivity and -growth, for a given parameter . The existence of Dirichlet weak solutions was obtained in [2], in the cases if or if , being the dimension of the domain. In this paper, with help of some new estimates...
Igor Bock, Jiří Jarušek (2007)
Applications of Mathematics
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The solvability of the contact problem is proved provided the plate is simply supported. The singular memory material is assumed. This makes it possible to get a priori estimates important for the strong convergence of gradients of velocities of solutions to the penalized problem.
Lopes Frota, Cícero (1994)
Portugaliae Mathematica
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G. Ströhmer, W. Zajączkowski (1999)
Applicationes Mathematicae
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Local existence of solutions is proved for equations describing the motion of a viscous compressible barotropic and self-gravitating fluid in a domain bounded by a free surface. First by the Galerkin method and regularization techniques the existence of solutions of the linearized momentum equations is proved, next by the method of successive approximations local existence to the nonlinear problem is shown.